Actually, I believe basic contract law requires he take at least a nominal salary so that he can be classified as a employee of the Federal government. He receives compensation ($1.00)and benefits ($$$$$$$$$$$$$$) and, in return, is expected to faithfully perform the duties of President of the United States. Upon completion of his term in office, he is then entitles to all the privileges and benefits ex-presidents enjoy.
Heard that on “60 Minutes,” but not exactly a salary in the usual sense.